Distance & Midpoint Formulas Sections covered: 1.8 The Coordinate Plane.
1-6 Midpoint and distance in the coordinate plane.
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Transcript of 1-6 Midpoint and distance in the coordinate plane.
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CHAPTER 11-6 Midpoint and distance in the
coordinate plane
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OBJECTIVES Students will be able to : Develop and apply the formula for
midpoint.
Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.
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MIDPOINT FORMULA What is the midpoint ? Answer: It is the middle section of a line.
Is what divides a line in 2 congruent sections.
How can you find the midpoint of a line? You can find the midpoint of a segment by
using the coordinates of its endpoints. Calculate the average of the x-coordinates
and the average of the y-coordinates of the endpoints.
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MIDPOINT FORMULA
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EXAMPLE 1 Find the coordinates of the
midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
Solution: midpoint formula
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EXAMPLE 2 Find the coordinates of the
midpoint of EF with endpoints E(–2, 3) and F(5, –3).
Solution: midpoint formula
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STUDENT GUIDE Do problems 2 and3 from page 47 from
book
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EXAMPLE 3 Lets do problems 1 and 2 from
worksheet
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STUDENT GUIDE Lets do problems 3 to 5 from worksheet
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EXAMPLE 4 M is the midpoint of XY. X has
coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.
Solution:
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STUDENT GUIDED PRACTICE Lets do problems 4 to 5 from book page
47 Worksheet problems 21-23
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DISTANCE FORMULA What is the distance formula? . The Distance Formula is used to
calculate the distance between two points in a coordinate plane.
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EXAMPLE 5 Lets do distance formula worksheet
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PYTHAGOREAN THEOREM What is the Pythagorean theorem? Answer: Is the theorem we used in right
triangles to figure out a side of the triangle. You can also used it to find the distance
between two points in the coordinate plane. In a right triangle, the two sides that form
the right angle are the legs. The side across from the right angle that stretches from one leg to the other is the hypotenuse. In the diagram, a and b are the lengths of the shorter sides, or legs, of the right triangle. The longest side is called the hypotenuse and has length c.
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EXAMPLE 6 Use the Distance Formula and
the Pythagorean Theorem to find the distance, to the nearest tenth, from R to S.
R(3, 2) and S(–3, –1)
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EXAMPLE 6 CONTINUE Method 1 Use the Distance Formula. Substitute
the values for the coordinates of R and S into the Distance Formula.
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EXAMPLE 6 CONTINUE Method 2 Use the Pythagorean Theorem. Count
the units for sides a and b.
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EXAMPLE 7 DO problems 1-2 in worksheet
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STUDENT GUIDED PRACTICE Let students do Pythagorean
workshweet
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PYTHAGOREAN A player throws the ball from
first base to a point located between third base and home plate and 10 feet from third base.
What is the distance of the throw, to the nearest tenth?
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HOMEWORK DO problems 8-15 in the book page 47
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CLOSURE Today we saw the midpoint formula, the
distance formula and the Pythagorean Theorem.